Probability Theory and Related Fields

, Volume 133, Issue 1, pp 1–17

Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees


DOI: 10.1007/s00440-004-0407-2

Cite this article as:
Aldous, D., Miermont, G. & Pitman, J. Probab. Theory Relat. Fields (2005) 133: 1. doi:10.1007/s00440-004-0407-2


We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.

Mathematics Subject Classification (2000)

60C05 60F17 

Key words or phrases

Random mapping Weak convergence Inhomogeneous continuum random tree 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of StatisticsU.C. BerkeleyUSA
  2. 2.CNRSUniversité Paris-SudOrsayFrance
  3. 3.Department of StatisticsU.C. BerkeleyUSA

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